The quantum magnetotransport properties of a nondegenerate two-dimensional gas of electrons interacting with helium-vapor atoms above a liquid-helium surface is studied in magnetic fields up to 20 T by the ac capacitive coupling technique. The data and the theoretical analysis performed show that in the ultraquantum limit the generalized or effective collision frequency νeff of the electrons increases faster with magnetic field than the cyclotron frequency ωc. Under extremely strong magnetic fields, where the Landau level width becomes comparable to or larger than the thermal energy, the high-cyclotron-frequency approximation ωcνeff, usually assumed in quantum transport theories, is no longer valid. The self-consistent Born-approximation theory is extended to be valid for any ratio of ωc to νeff. Then it describes the data perfectly without any adjustable parameter. The results reported here also give strong support to the universality of the linear Hall resistivity.